Currently no standard treatment exists for Fabry disease. The major clinical signs and symptoms of Fabry disease include skin lesions, benign corneal and lenticular opacities, excruciating acral pain, parethesias, autonomic dysfunction, cardiac disease, and renal failure. The primary objectives of this study are to demonstrate the long-term safety of r-halpha-Gal in patients with Fabry disease as determined by adverse experiences/events, vital signs, EKGs, echocardiograms, and clinical laboratory parameters. We will then demonstrate the continued efficacy of treatment in reducing GL-3 from the capillary endothelium of kidney, heart, and skin tissue.